Pedro Concei��o
University of Texas Inequality Project, The University of Texas at Austin
Center for Innovation, Technology and Policy Research, IST, Lisbon, Portugal

POSITION STATEMENT

What Lies Behind an Aggregate National Inequality Measure? Wage Inequality Patterns in the US: A Dynamic Analysis Across Counties and States

The literature on economic inequality often considers countries as the unit of analysis. Many studies focus on the evolution of a single national inequality measure. Others compare national measures of inequality across countries. Looking at inequality beyond the national level can be useful in two ways. One is to aggregate countries into supra-national geographic regions. This is useful, for example, when one compares the US with Europe. While the standard practice is to compare the US with individual European countries, Galbraith, Concei��o, Ferreira and (1999) show that when one takes Europe as a single region to be compared with the US, the pan-European measure of inequality is higher than the US inequality measure. US to single European country comparisons often conclude that the US is more unequal than "Europe", but these comparisons fail to take into account the cross-country dispersions in the distribution of income in Europe. The second way in which it may be important to analyze inequality considering geographic units different from the national level is to go in the opposite direction: analyzing sub-national geographic regions. Especially in large and diverse countries, such as the US, a national measure of inequality can hide different patterns of inequality and different dynamics within and across regions in the same country.

Exploring the geographic heterogeneity in the patterns and dynamics of inequality "hidden" by a national measure requires choosing an indicator of inequality that allows the partition of an aggregate inequality measure into the contributions of inequality within each of the sub-national regions and of inequality across all of the sub-national regions. Of all coefficients available to account for inequality, only the Theil index has the property of additive decomposability (meaning that the index is equal to inequality between different groups plus the sum of the weighted within-group inequality)[1].

The properties of the Theil index are particularly well suited for exercises intended to explore the relationship between inequality within and across groups at different levels of aggregation (see Concei��o, Galbraith and Bradford (2000) for an analytical discussions of this statement). If we consider different levels of geographic aggregation (counties, states, census regions, all the way up to the national level) the Theil index provides a way to relate inequality at each level with inequality at any other level of aggregation.

We will illustrate these properties of the Theil index constructing several measures of economic inequality across US regions. At the most fundamental level we consider a national measure of inequality based on a cross-plant wage Theil restricted to manufacturing. Then we look at the dispersion in the distribution of wages within counties and between counties, and assess the relative contribution to US inequality of each of these two components. We move up to the state level, and perform the same type of analysis, comparing the dynamics of inequality within selected states with the evolution of the national measure of inequality.

Another advantage of the Theil index is that it clearly specifies the level of inequality as a relationship between wage shares. Since we are considering groups, both quantities and wages are (equally) important determinants of inequality, that is, both the number of units in the group and the level of wages of the group are important. Thus, as an example, the contribution of a large state to US inequality will, in all likelihood, be large, both to the within-state component and to the between-state component. But the Theil index allows for a separation of the "size" effect from the "pure inequality" effect. Therefore, continuing with the example of a large state, we can determine the extent to which the contribution to US inequality is being driven the sheer size of the state or by the level of wage dispersion within the state.

In conclusion, the main objective is to show how the Theil index can be used as a tool of analysis when a geographic dimension is added to the study of economic inequality. As an "accounting" tool, intended to separate the relative contributions to inequality of different geographic units at different levels of aggregation, the Theil index is difficult to surpass. However, there is no known statistical distribution for the Theil index, which may limit its application when statistical inference is required. This is an area where new research may extend even further the potential of the Theil index as a tool to link economic inequality with spatial analysis.

References:

Pedro Concei��o, James K. Galbraith, Peter Bradford (2000). The Theil Index in Sequences of Nested and Hierarchic Grouping Structures, University of Texas Inequality Project Working Paper No. 15; available on the Internet at: http://utip.gov.utexas.edu.

James K. Galbraith, Pedro Concei��o, Pedro Ferreira (1999), "Inequality and Unemployment in Europe: The American Cure," New Left Review, 237(September/October): 28-51. �

[1] We are restricting the set of choices of coefficients to those that satisfy the three "standard" axioms of inequality measures: homogeneity, symmetry, and Pigou-Dalton. In fact, the Theil index is only the most commonly used indicator of the family of entropy-based inequality measures, all of which satisfy the three standard axioms plus additive decomposability.